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A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems, with Convergence Proofs

Sungwoo Park (swpark81***at***gmail.com)
Dianne P. O'Leary (oleary***at***cs.umd.edu)

Abstract: We present an infeasible primal-dual interior point method for semidefinite optimization problems, making use of constraint reduction. We show that the algorithm is globally convergent and has polynomial complexity, the first such complexity result for primal-dual constraint reduction algorithms for any class of problems. Our algorithm is a modification of one with no constraint reduction due to Potra and Sheng (1998) and can be applied whenever the data matrices are block diagonal. It thus solves as special cases any optimization problem that is a linear, convex quadratic, convex quadratically constrained, or second-order cone problem.

Keywords: semidefinite programming, semidefinite optimization, interior point methods, constraint reduction, primal-dual interior point method, primal dual infeasible, polynomial complexity, linear programming, linear optimization, quadratic programming, quadratic optimization, second-order cone optimization, second order cone programming.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

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Entry Submitted: 08/26/2013
Entry Accepted: 08/27/2013
Entry Last Modified: 02/19/2015

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